Mathematics as Information Compression via the Matching and Unification of Patterns

Figure 6

A schematic representation of the way two instances of the pattern “INFORMATION” in a body of data may be unified to form a single “unified pattern,” shown just above the middle of the figure. To achieve lossless compression, the relatively short identifier “w62” may be assigned to the unified pattern “INFORMATION,” as shown below the middle of the figure. At the bottom of the figure, the original data may be compressed by replacing each instance of “INFORMATION” with a copy of the relatively short identifer, “w62” (adapted from Figure 2.3 in [5], with permission).